Chapter 13.4, Problem 46E

A regression analysis carried out to relate y = repair time for a water filtration system (hr) to x₁ = elapsed time since the previous service (months) and x₂ = type of repair (1 if electrical and 0 if mechanical) yielded the following model based on n = 12 observations: y = .950 + .400x₁ + 1.250x₂. In addition, SST = 12.72, SSE = 2.09, and $s_{{\hat{\beta }}_2}=.312$.

a.    Does there appear to be a useful linear relationship between repair time and the two model predictors? Carry out a test of the appropriate hypotheses using a significance level of .05.

b.    Given that elapsed time since the last service remains in the model, does type of repair provide useful information about repair time? State and test the appropriate hypotheses using a significance level of .01.

c.    Calculate and interpret a 95% CI for β₂.

d.    The estimated standard deviation of a prediction for repair time when elapsed time is 6 months and the repair is electrical is .192. Predict repair time under these circumstances by calculating a 99% prediction interval. Does the interval suggest that the estimated model will give an accurate prediction? Why or why not?